Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Based on the very recent work by Censor and Segal (2009), and inspired by Xu (2006), Zhao and Yang (2005) , and Bauschke and Combettes (2001), we introduce and analyze an algorithm for solving the split common fixed-point problem for the wide class of quasi-nonexpansive operators in Hilbert spaces. Our results improve and develop previously discussed feasibility problems and related algorithms.
ISSN: 0362-546X

hal-00776645
https://hal.univ-antilles.fr/hal-00776645
DOI : 10.1016/j.na.2011.03.041

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
The aim of this note consists in studying the solvability of the following problem find xA such that yT(x) T is a maximal monotone operator and A a subspace of a real Hilbert space H.
ISSN: 0163-0563

hal-00779243
https://hal.univ-antilles.fr/hal-00779243
DOI : 10.1080/01630569508816642

Éditeur(s) : HAL CCSD Hindawi Publishing Corporation
Résumé : International audience
This paper is concerned with the study of a penalization-gradient algorithmfor solving variational inequalities, namely, find x ∈ C such that Ax, y − x ≥ 0 for all y ∈ C, where A : H → H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ : H → ∪ { ∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter βk, we consider an algorithm which alternates a proximal step with respect to ∂Ψ and a gradient step with respect to A and reads as xk I λkβk∂Ψ −1 xk−1 − λkAxk−1 . Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing themultivalued operator by its Yosida approximatewhich is always Lipschitz continuous.
ISSN: 0161-1712

hal-00776654
https://hal.univ-antilles.fr/hal-00776654
https://hal.univ-antilles.fr/hal-00776654/document
https://hal.univ-antilles.fr/hal-00776654/file/305856.pdf
DOI : 10.1155/2011/305856

Éditeur(s) : HAL CCSD
Résumé : International audience
Topological Methods in Nonlinear Analysis

hal-00699219
https://hal.archives-ouvertes.fr/hal-00699219

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Identifying operators with their graphs, we study the continuity of the parallel sum of two monotone operators with respect to set convergence and we examine its stability from a quantitative point of view.
Journal of Mathematical Analysis and applications

hal-00816097
https://hal.univ-antilles.fr/hal-00816097
DOI : 10.1006/jmaa.1996.0155

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
Recently Auslender & Crouzeix introduced a well-behaved asymptotical notion for convex functions. The aim of this work is to extend this notion to the saddle case
ISSN: 0163-0563

hal-00773195
https://hal.univ-antilles.fr/hal-00773195
DOI : 10.1080/01630569708816806

Éditeur(s) : HAL CCSD
Résumé : In this note we show that the splitting scheme of Passty [7] as well as the barycentric-proximal method of Lehdili & Lemaire [4] can be used to approximate a zero of the extended sum of maximal monotone operators. When the extended sum is maximal monotone, we extend the convergence result obtained by Lehdili & Lemaire for convex functions to the case of maximal monotone operators. Moreover, we recover the main convergence results by Passty and Lehdili & Lemaire when the pointwise sum of the involved operators is maximal monotone.
https://hal.univ-antilles.fr/hal-00783905

hal-00783905
https://hal.univ-antilles.fr/hal-00783905
https://hal.univ-antilles.fr/hal-00783905/document
https://hal.univ-antilles.fr/hal-00783905/file/10.1.1.165.7044.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Relying on prox-regularity we suggest and analyze a class of iterative schemes for solving nonconvex variational inequalities, our result can be considered as an improvement and a significant extension of previously known results in this field.
ISSN: 0096-3003

hal-00780630
https://hal.univ-antilles.fr/hal-00780630
DOI : 10.1016/j.amc.2003.06.003

Éditeur(s) : HAL CCSD
Résumé : SilviLaser 2015, La Grande Motte, FRA, 28-/09/2015 - 30/09/2015
International audience
The study provides technical guidelines to optimize sampling design parameters in the context of the implementation of biomass predictive models from airborne lidar data. Parameters under study were those easily controlled when implementing an area-based approach, i.e. lidar pulse density and both field sampling protocols and measurements. Parameters most impacting the model accuracy were identified by conducting a one-factor- at -a-time and a global sensitivity analyses. Number and size of field plot, and plot center position accuracy were identified to be the parameters most impacting model accuracy.
Proceedings of silviLaser 2015. Durrieu S. et Véga, C. (eds)
La Grande Motte, France

hal-01286833
https://hal.archives-ouvertes.fr/hal-01286833
https://hal.archives-ouvertes.fr/hal-01286833/document
https://hal.archives-ouvertes.fr/hal-01286833/file/mt2015-pub00046522.pdf
IRSTEA : PUB00046522

Éditeur(s) : HAL CCSD
Résumé : International audience
International Journal of Applied Mathematical Sciences

hal-01683258
https://hal.univ-antilles.fr/hal-01683258
DOI : 10.12988/ams.2013.13073

Éditeur(s) : HAL CCSD
Résumé : In this work, we develop a variant of a bundle method in order to find a zero of a maximal monotone operator. This algorithm relies on two polyhedral approximations of the epsilon-enlargement of the considered operator, via a systematic use of the transportation formula. Moreover, the use of a double polyhedral approximation in our algorithm could inspire other bundle methods for the case where the given operator can be split as the sum of two other maximal monotone operators.
https://hal.archives-ouvertes.fr/hal-00828930

hal-00828930
https://hal.archives-ouvertes.fr/hal-00828930
ARXIV : 1305.5810

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
ISSN: 1385-1292

hal-00493628
https://hal.archives-ouvertes.fr/hal-00493628

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Relying on the Yosida approximate, we investigate the problem of finding zeroes for a difference of two maximal monotone operators in Hilbert spaces. These zeroes are compared to those of the corresponding regularized and dual problems. The behavior of the regularized operator is also studied and a splitting algorithm involving the resolvents of both operators is suggested via a fixed-point formulation of the regularized problem. A particular attention is given to the DC programming case.
ISSN: 0096-3003

hal-00779986
https://hal.univ-antilles.fr/hal-00779986
DOI : 10.1016/j.amc.2008.01.024

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
A forward-backward inertial procedure for solving the problem of finding a zero of the sum of two maximal monotone operators is proposed and its convergence is established under a cocoercivity condition with respect to the solution set.
ISSN: 0377-0427

hal-00780778
https://hal.univ-antilles.fr/hal-00780778
https://hal.univ-antilles.fr/hal-00780778/document
https://hal.univ-antilles.fr/hal-00780778/file/10.1.1.12.4189.pdf
DOI : 10.1016/S0377-0427(02)00906-8

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Relying on the resolvent operator method and using Nadler's theorem, we suggest and analyze a class of iterative schemes for solving multivalued quasi-variational inclusions. In fact, by considering problems involving composition of mutivalued operators and by replacing the usual compactness condition by a weaker one, our result can be considered as an improvement and a significant extension of previously known results in this field.
ISSN: 1385-1292

hal-00815511
https://hal.univ-antilles.fr/hal-00815511
DOI : 10.1023/B:POST.0000023199.34934.9f

Éditeur(s) : HAL CCSD
Résumé : International audience
Communications on applied nonlinear analysis

hal-00815510
https://hal.univ-antilles.fr/hal-00815510

Éditeur(s) : HAL CCSD Heldermann
Résumé : International audience
We present an iterative method for finding zeroes of maximal monotone operators in a real Hilbert space. The underlying idea relies upon the discretization of a first order dissipative dynamical system which allows us to preserve the local feature, as well as to obtain convergence results. The main theorems do not only recover known convergence results of standard and inertial proximal methods, but also provide a theoretical basis for the application of new iterative methods.
Journal of Convex Analysis

hal-00780210
https://hal.univ-antilles.fr/hal-00780210

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
This article is concerned with a generalization of the hybrid steepest descent method from variational inequalities to the multivalued case. This will be reached by replacing the multivalued operator by its Yosida approximate, which is always Lipschitz continuous. It is worth mentioning that the hybrid steepest descent method is an algorithmic solution to variational inequality problems over the fixed point set of certain nonexpansive mappings and has remarkable applicability to the constrained nonlinear inverse problems like image recovery and MIMO communication systems
ISSN: 0163-0563

hal-00776641
https://hal.univ-antilles.fr/hal-00776641
DOI : 10.1080/01630563.2011.619676

Éditeur(s) : HAL CCSD
Résumé : The midpoint method was previously used in the solving of equations and in this work, the aim is to adapt the theory to the set-valued analysis in order to approach solutions of generalized equations of the form 0_inf(x)+F(x). In particular, we show the existence and convergence fo sequences provided the second order derivative of the function f satisfies a Hölder condition, or a center-Hölder condition.
GDR MOA
Sainte-Anne, Guadeloupe

hal-00757686
https://hal.archives-ouvertes.fr/hal-00757686

Éditeur(s) : HAL CCSD
Résumé : The convex feasibility problem (CFP) is to find a member of the intersection of finitely many closed convex sets in Euclidean space. When the intersection is empty, one can minimize a proximity function to obtain an approximate solution to the problem. The split feasibility problem (SFP) and the split equality problem (SEP) are generalizations of the CFP. The approximate SFP (ASFP) and approximate SEP (ASEP) involve finding only approximate solutions to the SFP and SEP, respectively. We present here the SSEA, a simultaneous iterative algorithm for solving the ASEP. When this algorithm is applied to the ASFP it resembles closely, but is not equivalent to, the CQ algorithm. The SSEA involves orthogonal projection onto the given closed convex sets. The relaxed SSEA (RSSEA) is an easily implementable variant of the SSEA that uses orthogonal projection onto half-spaces at each step to solve the SEP. The perturbed version of the SSEA (PSSEA) is similar to the RSSEA, but uses orthogonal projection onto a sequence of epi-convergent closed convex sets.
https://hal.univ-antilles.fr/hal-00776640

Droits : info:eu-repo/semantics/OpenAccess
hal-00776640
https://hal.univ-antilles.fr/hal-00776640
https://hal.univ-antilles.fr/hal-00776640/document
https://hal.univ-antilles.fr/hal-00776640/file/CBAM10.pdf